If you just bought the phone, make an appointment with the closest genius bar. There should be one close to you. Take your phone with you, and after it is tested and found with a hardware fault or error, they might give you a new one.

You can use the Voice Memo app within the Utilities folder [or any other App with voice input] to see if the microphone is working.
If the microphone seems to be defect you can hand it in for warranty. Otherwise you should consult with AT&T about the problem you encounter.

I guess "Christmas card list" is a group within your Adressbook, right?
You can set iTunes to synchronize only selected groups, however this means you will have to put all contacts you want to synchronize within one group.
To synchronize only selected groups open up iTunes and click on your iPhone. Select the "Info" tab and then change the Contact sync options.